But the club have offered deals to defenders Jonathan Burn and Kieran Weledji, midfielder Mark Kitching and striker James Warnett.

Parnaby, who returned for a second spell at the club in July 2012, made a total of 158 appearances, while former Leeds full-back Richardson made just one appearance under Karanka before spending the last three months on loan at Ipswich.

Nate Chalobah, Danny Graham, Tomas Mejias, Kenneth Omeruo and Jozsef Varga, all on loan at the club, have returned to their parent clubs.